[Merged by Bors] - feat: Intercalate a simplex between a point and a neighborhood by YaelDillies · Pull Request #14660 · leanprover-community/mathlib4

YaelDillies · 2024-07-11T19:50:52Z

... in finite dimensions.

depends on: [Merged by Bors] - chore: Move smooth_barycentric_coord #14666
depends on: [Merged by Bors] - feat: Translation of affine bases #14682
depends on: [Merged by Bors] - feat: Scaling of affine bases #14863

This will be used to show that convex functions are continuous.

github-actions · 2024-07-11T19:51:32Z

PR summary 847548ac4b

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Convex.Normed	1402	1515	+113 (+8.06%)

Import changes for all files

Files	Import difference
322 files `Mathlib.Analysis.CStarAlgebra.GelfandDuality` `Mathlib.Probability.Process.HittingTime` `Mathlib.Algebra.Module.Zlattice.Covolume` `Mathlib.Analysis.InnerProductSpace.Spectrum` `Mathlib.Probability.BorelCantelli` `Mathlib.Analysis.SpecialFunctions.Complex.LogDeriv` `Mathlib.NumberTheory.LSeries.HurwitzZetaValues` `Mathlib.Analysis.SpecialFunctions.Gamma.Basic` `Mathlib.Probability.Variance` `Mathlib.Analysis.Complex.Angle` `Mathlib.LinearAlgebra.Matrix.PosDef` `Mathlib.Analysis.SpecialFunctions.Integrals` `Mathlib.NumberTheory.Harmonic.ZetaAsymp` `Mathlib.Dynamics.Ergodic.AddCircle` `Mathlib.Analysis.Calculus.BumpFunction.Convolution` `Mathlib.Analysis.Fourier.PoissonSummation` `Mathlib.Analysis.InnerProductSpace.Rayleigh` `Mathlib.Analysis.SpecialFunctions.Trigonometric.Bounds` `Mathlib.Tactic.FunProp.ContDiff` `Mathlib.MeasureTheory.Integral.IntervalAverage` `Mathlib.Analysis.Distribution.FourierSchwartz` `Mathlib.Analysis.Calculus.ParametricIntervalIntegral` `Mathlib.Geometry.Manifold.VectorBundle.Tangent` `Mathlib.NumberTheory.GaussSum` `Mathlib.Geometry.Manifold.Diffeomorph` `Mathlib.MeasureTheory.Measure.Lebesgue.Complex` `Mathlib.NumberTheory.EulerProduct.DirichletLSeries` `Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology` `Mathlib.MeasureTheory.Integral.IntervalIntegral` `Mathlib.Analysis.Complex.AbsMax` `Mathlib.Analysis.InnerProductSpace.ProdL2` `Mathlib.Probability.Kernel.Disintegration.CDFToKernel` `Mathlib.Geometry.Manifold.MFDeriv.Basic` `Mathlib.Analysis.CStarAlgebra.Spectrum` `Mathlib.Geometry.Manifold.Instances.Real` `Mathlib.Analysis.SpecialFunctions.Trigonometric.ComplexDeriv` `Mathlib.Geometry.Manifold.Complex` `Mathlib.MeasureTheory.Integral.CircleIntegral` `Mathlib.Probability.StrongLaw` `Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique` `Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral` `Mathlib.Analysis.SpecialFunctions.Gamma.Beta` `Mathlib.MeasureTheory.Integral.TorusIntegral` `Mathlib.Geometry.Manifold.MFDeriv.FDeriv` `Mathlib.MeasureTheory.Function.L2Space` `Mathlib.MeasureTheory.Measure.LevyProkhorovMetric` `Mathlib.Analysis.Complex.TaylorSeries` `Mathlib.Analysis.Normed.Algebra.Spectrum` `Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions` `Mathlib.Analysis.FunctionalSpaces.SobolevInequality` `Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan` `Mathlib.Analysis.CStarAlgebra.Module.Constructions` `Mathlib.Probability.Distributions.Exponential` `Mathlib.Analysis.SpecialFunctions.Complex.Arctan` `Mathlib.Analysis.BoxIntegral.Partition.Measure` `Mathlib.Probability.Kernel.Composition` `Mathlib.Probability.Martingale.Upcrossing` `Mathlib.Probability.Martingale.OptionalSampling` `Mathlib.MeasureTheory.Integral.DivergenceTheorem` `Mathlib.Analysis.SpecialFunctions.Log.NegMulLog` `Mathlib.NumberTheory.NumberField.EquivReindex` `Mathlib.MeasureTheory.Measure.LogLikelihoodRatio` `Mathlib.NumberTheory.SiegelsLemma` `Mathlib.Analysis.SpecialFunctions.ImproperIntegrals` `Mathlib.Analysis.InnerProductSpace.Dual` `Mathlib.RingTheory.Polynomial.Hermite.Gaussian` `Mathlib.Analysis.Fourier.ZMod` `Mathlib.Analysis.SpecialFunctions.Complex.LogBounds` `Mathlib.Analysis.SpecialFunctions.Gamma.Deligne` `Mathlib.Analysis.Complex.PhragmenLindelof` `Mathlib.NumberTheory.ModularForms.JacobiTheta.Manifold` `Mathlib.Analysis.InnerProductSpace.NormPow` `Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls` `Mathlib.MeasureTheory.Integral.FundThmCalculus` `Mathlib.Probability.Kernel.Disintegration.Integral` `Mathlib.NumberTheory.LSeries.HurwitzZetaEven` `Mathlib.Analysis.CStarAlgebra.Matrix` `Mathlib.Geometry.Manifold.PoincareConjecture` `Mathlib.MeasureTheory.Measure.Portmanteau` `Mathlib.NumberTheory.LSeries.Deriv` `Mathlib.MeasureTheory.Measure.Haar.NormedSpace` `Mathlib.Analysis.Fourier.AddCircle` `Mathlib.Analysis.SpecialFunctions.Gaussian.PoissonSummation` `Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar` `Mathlib.Analysis.Fourier.Inversion` `Mathlib.Analysis.Normed.Algebra.QuaternionExponential` `Mathlib.Computability.AkraBazzi.AkraBazzi` `Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow` `Mathlib.Probability.Kernel.WithDensity` `Mathlib.Analysis.SpecialFunctions.NonIntegrable` `Mathlib.Geometry.Euclidean.Angle.Oriented.Basic` `Mathlib.Geometry.Euclidean.Sphere.Ptolemy` `Mathlib.Analysis.Normed.Algebra.MatrixExponential` `Mathlib.MeasureTheory.Group.AddCircle` `Mathlib.Probability.Independence.ZeroOne` `Mathlib.Analysis.SpecialFunctions.Complex.Analytic` `Mathlib.NumberTheory.ModularForms.EisensteinSeries.Basic` `Mathlib.Analysis.Convex.Cone.Pointed` `Mathlib.Probability.Kernel.Disintegration.StandardBorel` `Mathlib.MeasureTheory.Measure.Hausdorff` `Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Restrict` `Mathlib.Probability.Distributions.Gaussian` `Mathlib.Probability.Kernel.CondDistrib` `Mathlib.MeasureTheory.Measure.Haar.Unique` `Mathlib.Geometry.Manifold.BumpFunction` `Mathlib.Probability.Martingale.Basic` `Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho` `Mathlib.MeasureTheory.Decomposition.RadonNikodym` `Mathlib.Probability.Kernel.RadonNikodym` `Mathlib.NumberTheory.Harmonic.GammaDeriv` `Mathlib.Geometry.Manifold.ContMDiffMFDeriv` `Mathlib.MeasureTheory.Decomposition.SignedLebesgue` `Mathlib.MeasureTheory.Measure.WithDensityFinite` `Mathlib.Geometry.Euclidean.Sphere.Power` `Mathlib.Analysis.Complex.CauchyIntegral` `Mathlib.Analysis.SpecialFunctions.Pow.Deriv` `Mathlib.Analysis.SpecialFunctions.PolarCoord` `Mathlib.MeasureTheory.Covering.LiminfLimsup` `Mathlib.Geometry.Euclidean.Angle.Sphere` `Mathlib.Analysis.InnerProductSpace.LinearPMap` `Mathlib.MeasureTheory.Order.UpperLower` `Mathlib.Analysis.Calculus.ParametricIntegral` `Mathlib.Probability.Martingale.Convergence` `Mathlib.Analysis.Complex.UpperHalfPlane.Metric` `Mathlib.Geometry.Manifold.MFDeriv.UniqueDifferential` `Mathlib.Probability.Kernel.IntegralCompProd` `Mathlib.NumberTheory.ModularForms.JacobiTheta.OneVariable` `Mathlib.MeasureTheory.Function.AEEqOfIntegral` `Mathlib.Probability.Kernel.Disintegration.CondCDF` `Mathlib.Probability.Kernel.Disintegration.Density` `Mathlib.Analysis.Convex.Integral` `Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace` `Mathlib.MeasureTheory.Function.SpecialFunctions.Arctan` `Mathlib.MeasureTheory.Constructions.Prod.Integral` `Mathlib.NumberTheory.Cyclotomic.Embeddings` `Mathlib.MeasureTheory.Integral.Layercake` `Mathlib.Geometry.Euclidean.Circumcenter` `Mathlib.Analysis.CStarAlgebra.Module.Defs` `Mathlib.Analysis.Complex.Schwarz` `Mathlib.Analysis.Fourier.FourierTransformDeriv` `Mathlib.Analysis.Complex.UpperHalfPlane.Manifold` `Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace` `Mathlib.NumberTheory.LSeries.RiemannZeta` `Mathlib.MeasureTheory.Covering.OneDim` `Mathlib.Data.Real.Pi.Leibniz` `Mathlib.Geometry.Euclidean.Inversion.Calculus` `Mathlib.Analysis.InnerProductSpace.Positive` `Mathlib.NumberTheory.NumberField.Units.Basic` `Mathlib.Probability.Kernel.Invariance` `Mathlib.Probability.Distributions.Uniform` `Mathlib.Geometry.Euclidean.Sphere.SecondInter` `Mathlib.Geometry.Euclidean.Basic` `Mathlib.MeasureTheory.Covering.DensityTheorem` `Mathlib.MeasureTheory.Constructions.UnitInterval` `Mathlib.NumberTheory.Liouville.Measure` `Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique` `Mathlib.NumberTheory.DirichletCharacter.GaussSum` `Mathlib.Probability.Kernel.MeasurableIntegral` `Mathlib.Geometry.Euclidean.MongePoint` `Mathlib.NumberTheory.ModularForms.JacobiTheta.Bounds` `Mathlib.Geometry.Euclidean.Sphere.Basic` `Mathlib.Geometry.Euclidean.Angle.Unoriented.RightAngle` `Mathlib.NumberTheory.ModularForms.EisensteinSeries.MDifferentiable` `Mathlib.NumberTheory.LSeries.Dirichlet` `Mathlib.Algebra.Module.Zlattice.Basic` `Mathlib.Analysis.InnerProductSpace.Projection` `Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog` `Mathlib.Tactic.NormNum.LegendreSymbol` `Mathlib.Analysis.SpecialFunctions.BinaryEntropy` `Mathlib.NumberTheory.ModularForms.JacobiTheta.TwoVariable` `Mathlib.Analysis.Fourier.RiemannLebesgueLemma` `Mathlib.Analysis.SpecialFunctions.SmoothTransition` `Mathlib.Analysis.BoxIntegral.Basic` `Mathlib.Analysis.Quaternion` `Mathlib.Analysis.SpecialFunctions.Trigonometric.Complex` `Mathlib.Analysis.BoxIntegral.Integrability` `Mathlib.Analysis.InnerProductSpace.Calculus` `Mathlib.Combinatorics.Additive.AP.Three.Behrend` `Mathlib.Analysis.Complex.Polynomial.Basic` `Mathlib.MeasureTheory.Integral.IntegralEqImproper` `Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic` `Mathlib.Probability.Kernel.Disintegration.Basic` `Mathlib.Analysis.Complex.RemovableSingularity` `Mathlib.MeasureTheory.Measure.Tilted` `Mathlib.Analysis.Complex.Liouville` `Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.GaussSum` `Mathlib.Geometry.Euclidean.Angle.Oriented.RightAngle` `Mathlib.NumberTheory.LSeries.MellinEqDirichlet` `Mathlib.Analysis.InnerProductSpace.MeanErgodic` `Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol` `Mathlib.MeasureTheory.Function.Jacobian` `Mathlib.Analysis.Complex.LocallyUniformLimit` `Mathlib.Analysis.InnerProductSpace.EuclideanDist` `Mathlib.NumberTheory.Harmonic.EulerMascheroni` `Mathlib.Probability.Moments` `Mathlib.Analysis.SpecialFunctions.Log.Deriv` `Mathlib.NumberTheory.LegendreSymbol.AddCharacter` `Mathlib.Topology.MetricSpace.HausdorffDimension` `Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff` `Mathlib.Analysis.InnerProductSpace.PiL2` `Mathlib.NumberTheory.LegendreSymbol.QuadraticReciprocity` `Mathlib.Analysis.SpecialFunctions.Gamma.BohrMollerup` `Mathlib.Data.Real.Pi.Bounds` `Mathlib.MeasureTheory.Decomposition.Lebesgue` `Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation` `Mathlib.Geometry.Manifold.MFDeriv.Defs` `Mathlib.NumberTheory.ModularForms.Basic` `Mathlib.Probability.Process.Stopping` `Mathlib.MeasureTheory.Integral.PeakFunction` `Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1` `Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2` `Mathlib.Analysis.Normed.Algebra.Basic` `Mathlib.MeasureTheory.Integral.ExpDecay` `Mathlib.Analysis.SpecialFunctions.Stirling` `Mathlib.Analysis.ODE.Gronwall` `Mathlib.Analysis.ConstantSpeed` `Mathlib.LinearAlgebra.Matrix.Hermitian` `Mathlib.Analysis.Calculus.Monotone` `Mathlib.RingTheory.Polynomial.Selmer` `Mathlib.Geometry.Manifold.IntegralCurve` `Mathlib.Analysis.SumIntegralComparisons` `Mathlib.MeasureTheory.Constructions.HaarToSphere` `Mathlib.Analysis.SpecialFunctions.JapaneseBracket` `Mathlib.MeasureTheory.Integral.CircleTransform` `Mathlib.MeasureTheory.Integral.DominatedConvergence` `Mathlib.Probability.Kernel.MeasureCompProd` `Mathlib.NumberTheory.ZetaValues` `Mathlib.Analysis.SpecialFunctions.Arsinh` `Mathlib.Analysis.Fourier.FourierTransform` `Mathlib.LinearAlgebra.Matrix.LDL` `Mathlib.Tactic.FunProp.Differentiable` `Mathlib.Analysis.Matrix` `Mathlib.Probability.IdentDistrib` `Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances` `Mathlib.Analysis.Convolution` `Mathlib.LinearAlgebra.Matrix.SchurComplement` `Mathlib.Analysis.MellinInversion` `Mathlib.Analysis.Convex.Cone.InnerDual` `Mathlib.Analysis.Complex.Polynomial.UnitTrinomial` `Mathlib.Geometry.Manifold.PartitionOfUnity` `Mathlib.Geometry.Manifold.MFDeriv.Atlas` `Mathlib.MeasureTheory.Covering.Differentiation` `Mathlib.NumberTheory.LSeries.HurwitzZetaOdd` `Mathlib.Analysis.Complex.Hadamard` `Mathlib.Analysis.Calculus.LineDeriv.IntegrationByParts` `Mathlib.Combinatorics.SimpleGraph.LapMatrix` `Mathlib.Analysis.BoundedVariation` `Mathlib.Analysis.InnerProductSpace.Adjoint` `Mathlib.NumberTheory.WellApproximable` `Mathlib.MeasureTheory.Measure.Lebesgue.Basic` `Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order` `Mathlib.Analysis.Convex.Cone.Proper` `Mathlib.Probability.Process.Adapted` `Mathlib.Analysis.Convex.Cone.Closure` `Mathlib.MeasureTheory.Measure.Lebesgue.Integral` `Mathlib.Analysis.SpecialFunctions.Trigonometric.InverseDeriv` `Mathlib.Analysis.Calculus.Gradient.Basic` `Mathlib.Analysis.Calculus.Rademacher` `Mathlib.Analysis.Calculus.BumpFunction.InnerProduct` `Mathlib.LinearAlgebra.Matrix.Spectrum` `Mathlib.MeasureTheory.Integral.Pi` `Mathlib.NumberTheory.NumberField.House` `Mathlib.Analysis.InnerProductSpace.l2Space` `Mathlib.NumberTheory.NumberField.Embeddings` `Mathlib.Probability.Process.Filtration` `Mathlib.MeasureTheory.Integral.Periodic` `Mathlib.NumberTheory.Harmonic.Bounds` `Mathlib.Analysis.MellinTransform` `Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar` `Mathlib.MeasureTheory.Integral.Gamma` `Mathlib.Analysis.VonNeumannAlgebra.Basic` `Mathlib.Analysis.Convex.SpecificFunctions.Deriv` `Mathlib.Analysis.SpecialFunctions.Trigonometric.EulerSineProd` `Mathlib.Probability.Kernel.Condexp` `Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator` `Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv` `Mathlib.Geometry.Euclidean.Triangle` `Mathlib.MeasureTheory.Covering.Besicovitch` `Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension` `Mathlib.Probability.Distributions.Gamma` `Mathlib.Probability.Martingale.OptionalStopping` `Mathlib.Probability.Martingale.BorelCantelli` `Mathlib.Analysis.SpecialFunctions.ExpDeriv` `Mathlib.Probability.Density` `Mathlib.Analysis.Complex.OpenMapping` `Mathlib.Analysis.Calculus.BumpFunction.Normed` `Mathlib.Analysis.ODE.PicardLindelof` `Mathlib.Probability.ConditionalExpectation` `Mathlib.Analysis.SpecialFunctions.Trigonometric.ArctanDeriv` `Mathlib.Geometry.Manifold.LocalDiffeomorph` `Mathlib.Analysis.InnerProductSpace.Orientation` `Mathlib.Geometry.Euclidean.Angle.Oriented.Affine` `Mathlib.NumberTheory.LSeries.HurwitzZeta` `Mathlib.Tactic` `Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform` `Mathlib.MeasureTheory.Measure.Haar.Disintegration` `Mathlib.Analysis.Distribution.SchwartzSpace` `Mathlib.NumberTheory.Bertrand` `Mathlib.Analysis.BoxIntegral.DivergenceTheorem` `Mathlib.NumberTheory.LSeries.Convolution` `Mathlib.MeasureTheory.Measure.WithDensityVectorMeasure` `Mathlib.Analysis.SpecialFunctions.Pow.Integral` `Mathlib.Geometry.Manifold.WhitneyEmbedding` `Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic` `Mathlib.Probability.Kernel.Disintegration.Unique` `Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus` `Mathlib.Probability.Independence.Conditional` `Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic` `Mathlib.MeasureTheory.Function.ConditionalExpectation.Real` `Mathlib.Data.Real.Pi.Wallis` `Mathlib.Probability.Process.PartitionFiltration` `Mathlib.Probability.Notation` `Mathlib.NumberTheory.LSeries.AbstractFuncEq` `Mathlib.Probability.CDF` `Mathlib.MeasureTheory.Measure.Haar.OfBasis` `Mathlib.Data.Complex.ExponentialBounds` `Mathlib.Analysis.InnerProductSpace.TwoDim` `Mathlib.Probability.Martingale.Centering` `Mathlib.MeasureTheory.Measure.Haar.Quotient` `Mathlib.Geometry.Manifold.Instances.Sphere` `Mathlib.Geometry.Manifold.VectorBundle.SmoothSection` `Mathlib.Analysis.InnerProductSpace.LaxMilgram`	1
`Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable`	8
`Mathlib.NumberTheory.Cyclotomic.PrimitiveRoots` `Mathlib.NumberTheory.Cyclotomic.Gal`	16
`Mathlib.RingTheory.LittleWedderburn`	25
`Mathlib.RingTheory.Polynomial.Cyclotomic.Eval` `Mathlib.NumberTheory.PrimesCongruentOne`	26
`Mathlib.NumberTheory.Liouville.LiouvilleWith`	29
3 files `Mathlib.NumberTheory.Liouville.LiouvilleNumber` `Mathlib.NumberTheory.Liouville.Basic` `Mathlib.NumberTheory.Liouville.Residual`	32
`Mathlib.NumberTheory.ModularForms.EisensteinSeries.UniformConvergence` `Mathlib.NumberTheory.ModularForms.EisensteinSeries.IsBoundedAtImInfty`	51
`Mathlib.Analysis.Complex.UpperHalfPlane.Topology`	55
`Mathlib.Analysis.Calculus.Taylor`	68
`Mathlib.Geometry.Euclidean.Angle.Unoriented.Affine`	75
`Mathlib.Analysis.InnerProductSpace.Symmetric` `Mathlib.Analysis.Calculus.SmoothSeries`	76
4 files `Mathlib.Analysis.Calculus.InverseFunctionTheorem.ContDiff` `Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic` `Mathlib.Geometry.Euclidean.Angle.Unoriented.Conformal` `Mathlib.Analysis.Complex.Arg`	77
11 files `Mathlib.Analysis.InnerProductSpace.OfNorm` `Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner` `Mathlib.Analysis.InnerProductSpace.Basic` `Mathlib.Analysis.InnerProductSpace.Orthogonal` `Mathlib.Analysis.Convex.Strong` `Mathlib.Geometry.Euclidean.Inversion.ImageHyperplane` `Mathlib.MeasureTheory.Function.SpecialFunctions.Inner` `Mathlib.Analysis.Calculus.Conformal.InnerProduct` `Mathlib.Geometry.Euclidean.Inversion.Basic` `Mathlib.Analysis.InnerProductSpace.ConformalLinearMap` `Mathlib.Geometry.Euclidean.PerpBisector`	78
`Mathlib.Analysis.Calculus.ContDiff.RCLike`	79
`Mathlib.Analysis.Calculus.UniformLimitsDeriv`	81
5 files `Mathlib.Analysis.Calculus.MeanValue` `Mathlib.Analysis.Calculus.LHopital` `Mathlib.Analysis.Calculus.FDeriv.Extend` `Mathlib.Analysis.Convex.Deriv` `Mathlib.Analysis.Calculus.FDeriv.Symmetric`	83
`Mathlib.Analysis.Convex.GaugeRescale`	102
`Mathlib.Analysis.Convex.StrictConvexBetween`	106
`Mathlib.Analysis.Convex.AmpleSet`	107
`Mathlib.Analysis.Convex.StrictConvexSpace` `Mathlib.Analysis.Convex.Uniform`	109
`Mathlib.Analysis.Convex.Side` `Mathlib.Analysis.Convex.Normed`	113

Declarations diff

+ exists_mem_interior_convexHull_affineBasis

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

Mathlib/Analysis/Convex/Normed.lean

ghost · 2024-08-13T09:33:27Z

This PR/issue depends on:

~~[Merged by Bors] - chore: Move smooth_barycentric_coord #14666~~
~~[Merged by Bors] - feat: Translation of affine bases #14682~~
~~[Merged by Bors] - feat: Scaling of affine bases #14863~~
By Dependent Issues (🤖). Happy coding!

... in finite dimensions.

Mathlib/Analysis/Convex/Normed.lean

eric-wieser · 2024-08-22T22:11:23Z

Mathlib/Analysis/Convex/Normed.lean

+/-- We can intercalate a simplex between a point and one of its neighborhoods. -/
+lemma exists_mem_interior_convexHull_affineBasis (hs : s ∈ 𝓝 x) :
+    ∃ b : AffineBasis (Fin (finrank ℝ E + 1)) ℝ E,
+      x ∈ interior (convexHull ℝ (range b)) ∧ convexHull ℝ (range b) ⊆ s := by


Is there some stronger statement along the lines of "and the points of the simplex lie on the interior or frontier of s"?

Because of interior_mem_nhds, this lemma is easily strengthenable to ... ∧ convexHull ℝ (range b) ⊆ interior s. I don't think I should be making that a lemma though as the current is syntactically more general and the stronger one is easily derived.

I don't see an easy way of making the points of the simplices lie on the frontier of s, eg s = univ has empty frontier, or s = a halfspace has a very flat frontier.

eric-wieser

bors d+

Thanks!

mathlib-bors · 2024-08-22T22:11:31Z

✌️ YaelDillies can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

YaelDillies · 2024-08-23T09:30:57Z

bors merge

... in finite dimensions.

mathlib-bors · 2024-08-23T11:17:17Z

Pull request successfully merged into master.

Build succeeded:

... in finite dimensions.

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[Merged by Bors] - feat: Convex functions are continuous #14999

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feat: Intercalate a polyhedron between a point and a neighborhood

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[Merged by Bors] - feat: Intercalate a simplex between a point and a neighborhood#14660

[Merged by Bors] - feat: Intercalate a simplex between a point and a neighborhood#14660
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mathlib-bors bot commented Aug 22, 2024

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YaelDillies commented Jul 11, 2024 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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PR summary 847548ac4b

Import changes for modified files

Declarations diff

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ghost commented Aug 13, 2024

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YaelDillies Aug 23, 2024 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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YaelDillies commented Jul 11, 2024 •

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YaelDillies Aug 23, 2024 •

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